In a 5-quart (or larger) pot, heat water with half an onion, half a head of garlic, a little salt, and oregano.

Meanwhile, trim excess fat and skin from the chicken. When the water starts to boil, add the cleaned chicken, cut into quarters.

Cover and let it boil. Once the pot starts to whistle, cook for 15 minutes, then turn off the heat and let it cool before opening.

While waiting, rinse the hominy three times until the water runs clear.

Once you can open the pot, remove the chicken, onion, and garlic. Add the hominy to the chicken broth with a little more salt. Shred the chicken and discard the bones.

Cook the hominy for 25 minutes until the kernels are tender. Add the shredded chicken, check for salt, let it simmer for a few more minutes, and serve.

Chop the onion, lettuce, radishes, and limes. Serve with tostadas and serrano chiles or spicy salsa.